solve by substitution
7x-2y=35
x-4y=5
2x+y=9
8x+4y=36
for the first question:
x=4y+5
7(4y=5)-2y=35
28y+35-2y=35
26y=35-35
y=0
for x:
x-4y=5 (substitute)
x-o=5
x=5
(5,0)
if you want to check your answer just substitue it to any of the given linear equations. Goodluck!
To solve the system of equations by substitution, follow these steps:
1. Choose one equation and express one variable in terms of the other variable.
- Let's start with the first system of equations:
Equation 1: 7x - 2y = 35
Equation 2: x - 4y = 5
- From Equation 2, we can express x in terms of y as x = 4y + 5.
2. Substitute the expression found in step 1 into the other equation in the system.
- Substitute x = 4y + 5 into Equation 1:
7(4y + 5) - 2y = 35
28y + 35 - 2y = 35
26y + 35 = 35
3. Solve the resulting equation from step 2 to find the value of the remaining variable.
- Simplify the equation:
26y + 35 = 35
26y = 0
y = 0
4. Substitute the value of the variable found in step 3 back into one of the original equations to solve for the other variable.
- Substitute y = 0 into Equation 2:
x - 4(0) = 5
x = 5
5. Check the solution by substituting the values of the variables into the other original equation.
- Substitute x = 5 and y = 0 into Equation 1:
7(5) - 2(0) = 35
35 - 0 = 35
35 = 35
- The solution checks out because both sides of the equation are equal.
6. The solution to the first system of equations is x = 5 and y = 0.
Now, let's move on to the second system of equations:
1. Choose one equation and express one variable in terms of the other variable.
- Let's start with the second system of equations:
Equation 1: 2x + y = 9
Equation 2: 8x + 4y = 36
- From Equation 1, we can express y in terms of x as y = 9 - 2x.
2. Substitute the expression found in step 1 into the other equation in the system.
- Substitute y = 9 - 2x into Equation 2:
8x + 4(9 - 2x) = 36
8x + 36 - 8x = 36
36 = 36
3. Analyze the resulting equation from step 2.
- In this case, we end up with 36 = 36, which is always true. This means that the two original equations represent the same line, and there are infinitely many solutions.
4. The second system of equations has infinitely many solutions since the equations are dependent.
To summarize, the first system of equations has a unique solution: x = 5 and y = 0. The second system of equations has infinitely many solutions.